Horseshoe lemma

The Horseshoe Lemma is a result in topology and functional analysis, specifically in the context of the study of topological vector spaces. It is particularly important in the field of functional analysis, where it has applications in various areas including the theory of nonlinear operators and differential equations. The lemma generally states that under certain conditions, a continuous linear operator defined on a Banach space can be approximated by finite-dimensional spaces in a specific way.